How to enable CUDA on Ubunutu 14.04 for a GTX 970?
I got it working, and I can at least partially answer my questions:

Problem #1: There are two CUDA 6.5 packages at nvidia, a "normal" one and one "with Support for GeForce GTX9xx GPUs" (here). Choose the later one.

Problem #2: I had already installed the nvidia 343.22 driver from xorg/edgers. The CUDA packages comes with its own 343.19 (as well as its own nivdia-modprobe).

FYI: I've used the .deb file (not the .run one). This drops a handful of other .deb files onto the system, but does not install them. After apt-get update-ing they can be installed using: apt-get install cuda

I needed to bring the system into a terminal-only state where no nvidia driver was running in order to remove the 343.22 one and install the cuda package.

Regarding to my questions:


Blender does use the (external) CUDA install.
2.42b produces a black screen and an error message in the terminal, i.e. there is a code change needed for the GTX 970 to work
nvidia-modprobe is part of the package - i.e. no need to install it separately.